On this photograph, we can just about notice Venus' atmosphere, as a small ring of light; its gets mostly lost into the glare of the Sun. For exoplanets the task is even harder.
Instead of a resolved ring of light, we measure the size of the planet as a function of wavelength. For instance, observing just in blue light, we would notice that a given planet appears bigger, which we interpret as being more opaque and a signature of Rayleigh scattering (the process creating our blue skies). In this fashion, several molecules have been identified in exoplanets' atmospheres, even some clouds.
Our telescopes usually collect starlight combined with any reflected and re-emitted planetary light. During occultation, only starlight reaches Earth. Subtracting, we can recover an exoplanet's light and establish its spectrum.
In addition to retrieving chemical abundances, emission spectroscopy permits the reconstruction of the vertical structure of an exo-atmosphere. Eventually this will tell us whether the surface of a telluric planet allows the continuous presence of liquid water.
Hertzsprung-Russell diagrams plot the intrinsic luminosity of a star and its effective temperature. Stars form clumps, notably a main sequence from which we learned much about stellar evolution.
From a planet's flux (obtained at occultation) and its distance to Earth, we can compute its
intrinsic luminosity. The